8.2.2.4 Selecting the Inductor (L1)

The selection of the inductor affects steady state operation as well as transient behavior and loop stability. These factors make it the most important component in power regulator design. There are three important inductor specifications: inductor value, DC resistance and saturation current. Considering inductor value alone is not enough. Inductor values can have ±20% tolerance with no current bias. When the inductor current approaches saturation level, the effective inductance can fall to a fraction of the zero current value.

The minimum value of the inductor should be able to meet inductor current ripple (ΔI_L) requirement at worst case. In a boost converter, maximum inductor current ripple occurs at 50% duty cycle. For the applications where duty cycle is always smaller or larger than 50%, Equation 12 should be used with the duty cycle closest to 50% and corresponding input voltage to calculate the minimum inductance. For applications that need to operate with 50% duty cycle when input voltage is somewhere between the minimum and the maximum input voltage, Equation 13 should be used. K_IND is a coefficient that represents the amount of inductor ripple current relative to the maximum input current (I_INDC = I_Lavg). The maximum input current can be estimated with Equation 11, with an estimated efficiency based on similar applications (η_EST). The inductor ripple current will be filtered by the output capacitor. Therefore, choosing high inductor ripple currents will impact the selection of the output capacitor since the output capacitor must have a ripple current rating equal to or greater than the inductor ripple current. In general, the inductor ripple value (K_IND) is at the discretion of the designer. However, the following guidelines may be used.

For CCM operation, it is recommended to use K_IND values in the range of 0.2 to 0.4. Choosing K_IND closer to 0.2 results in a larger inductance value, maximizes the converter’s potential output current and minimizes EMI. Choosing K_IND closer to 0.4 results in a smaller inductance value, a physically smaller inductor, and improved transient response, but potentially worse EMI and lower efficiency. Using an inductor with a smaller inductance value may result in the converter operating in DCM. This reduces the boost converter’s maximum output current, causes larger input voltage and output voltage ripple and reduced efficiency. For this design, choose K_IND = 0.3 and a conservative efficiency estimate of 85% with the minimum input voltage and maximum output current. Equation 12 is used with the minimum input voltage because this corresponds to duty cycle closest to 50%. The maximum input current is estimated at 4.53A and the minimum inductance is 1.68 µH. A standard value of
2.2 µH is chosen.

Equation 11.

Equation 12.

Equation 13.

After choosing the inductance, the required current ratings can be calculated. The inductor will be closest to its ratings with the minimum input voltage. The ripple with the chosen inductance is calculated with Equation 14. The RMS and peak inductor current can be found with Equation 15 and Equation 16. For this design the current ripple is 1.04 A, the RMS inductor current is 4.53 A, and the peak inductor current is 5.05 A. It is generally recommended for the peak inductor current rating of the selected inductor be 20% higher to account for transients during power up, faults or transient load conditions. The most conservative approach is to specify an inductor with a saturation current greater than the maximum peak current limit of the TPS55330. This helps to avoid saturation of the inductor. The chosen inductor is a Würth Elektronik 74437346022. It has a saturation current rating of 15 A, RMS current rating of 6.5 A, and typical DCR of 18 mΩ.

Equation 14.

Equation 15.

Equation 16.

The TPS55330 has built-in slope compensation to avoid subharmonic oscillation associated with current mode control. If the inductor value is too small, the slope compensation may not be adequate, and the loop can be unstable.